This article proposes the development of 'digital reflexive sociology', that is, the use of digital methods and Big Data to systematically understand the social and historical conditions of sociologists. To show the potential of this approach, the group of 500 sociologists who have their biographies written in 10 or more languages within Wikipedia is studied. Computational methods were used to extract temporal, spatial and relational information from these biographies in order to construct a general historical account of the discipline. The analysis shows various structural patterns of 'collectively remembered' sociology: historical changes in the frequency of globally recognized sociologists, trends in gender composition, degrees of diffusion and centrality of the main referents, geographical concentrations of the discipline, disciplinary differentiation in networks of greater biographical connectivity, flows of biographical references between countries, and birth-death migration patterns. Considering the temporal evolution of these aspects, we distinguish five generations of sociologists who shared similar collective circumstances. The record of high concentration (in terms of geography, gender and schools of thought) evidenced by the passing of these generations is highlighted. The results are discussed together with a more general reflection on the opportunities and limits of an eventual digital reflexive sociology.